The present invention relates generally to finite impulse response (FIR) filters, and more particularly, to a method of using staggered proportional plus delay, or posicast filters in satellite control systems, and the like, that provides for a reduction in resonances produced in the satellite systems during maneuvers and payload slewing.
The use of finite impulse response (FIR) filters to shape signals to improve system response is known in the art, and has been extensively elaborated. The simplest example is referred to as posicast control, or, in the satellite industry, as a "deadbeat" maneuver. In this method, it is desired to step a system with an undamped resonance of known frequency, without post-maneuver ringing. Half the step command amplitude is applied immediately, and the other half is applied half a resonance period later. The result is that the resonance excitation induced by the first command is canceled by that induced by the second command, resulting in zero net resonance excitation after the maneuver. This process can be thought of as passing the command through a proportional plus delay filter where the gain on both the proportional and the delayed channels is 1/2. Such a FIR filter is referred to as a "posicast" filter.
The earliest work on posicast filters was cast in a much more general framework. D. J. Gimpel and J. F. Calvert showed in "Signal Component Control", AIEE Trans. (Appl. Industry), Vol 71, Nov. 1952, pp. 339-343, how to design an FIR command filter to reduce multiple resonance modes (which could have damping) to zero in finite time for commands that were polynomial (e.g., step plus ramp plus parabolic). Their approach was to mathematically formulate filter objectives in terms of the filter coefficients, then solve for filter gains and delays. The objective that resonances be nulled in finite time was but one of three objectives they set, and they pointed out that the same technique could be used to realize other objectives as well. This work was included in U.S. Pat. No. 2,801,351, issued to Calvert et al., and the concept of using such filters in various locations in closed loop systems to improve their characteristics as covered in U.S. Pat. No. 3,010,035, issued to Calvert et al.
The effect of damping and of multiple resonant modes on the solution is that posicast filter gains shift slightly in value from 1/2, and that the command signal must be passed through a series of posicast filters, one for each mode. The appropriate filter gains and delays may be obtained by directly applying Calvert's technique, and the insight presented above is known in the art, and is described by Cook in an article entitled "Control of Flexible Structures via Posicast", Proceedings of the Eighteenth Southeastern Symposium on System Theory, Apr. 7-8, 1986, pp. 31-35.
A disadvantage of the single-delay posicast filter is that it is sensitive to knowledge of resonance frequency. The art described above does not address robustness to frequency range as a design consideration for posicast filters.
U.S. Pat. No. 4,916,635, entitled "Shaping Command Inputs to Minimize Unwanted Dynamics", issued to Singer et al., teaches how to design FIR filters to provide resonance attenuation when the frequencies are uncertain. The method taught therein is to add a requirement to the filter objectives that the derivatives of the output response to changes in the resonance frequency be zero. The filter characteristics are then solved for directly, as taught by Calvert. The resultant filters are directly equivalent to cascading an appropriate posicast filter with itself repeatedly. Calvert's patents are not cited, and posicast techniques are mentioned and dismissed as not being robust. There is no teaching of cascaded posicast filters and no indication that their scheme is functionally equivalent to cascading posicast filters with identical delay times. The filtering schemes of U.S. Pat. No. 4,916,635 are referred to herein as a "repeated posicast" scheme, a "double posicast" or three impulse scheme, and a "triple posicast" or four impulse scheme.
The approach of the Singer patent does not provide a maximal frequency range for a desired level of resonance reduction. An alternative approach that gives up the requirement that the resonance reduction for the nominal resonance be exactly zero in exchange for increasing the frequency range over which a desired level may be achieved, is described by Singer, et. al., in "Shaping Inputs to Reduce Vibration: A Vector Diagram Approach", Proceedings of the 1990 IEEE International Conference on Robotics and Automation, Cincinnati, Ohio, May 13-18, 1990, pp. 922-927. Again, the technique presented is to formulate the problem mathematically, and solve for the filter parameters. The frequency response of such filters resemble those produced by the present invention, and the relationship and differences will be detailed below.
The Singer paper is the closest prior art to the present invention. Both the paper and the present invention have as their goal the reduction in residual vibration magnitude to a prescribed level across a given band of frequencies. Both have as an aim improved dynamic response of flexible spacecraft to maneuvers. Both pass a command signal through a FIR filter to accomplish this end, and both methods produce filters whose frequency response up through a region of specified resonance attenuation is nearly identical.
It is also believed that (non-posicast, infinite impulse response) notch filters, including high-order filters, have been used for command shaping. Such filters take longer to reduce vibration to the level produced by a FIR filter, and are not easily applicable to fixed amplitude actuators, such as thrusters and stepper motors employed in satellite control systems.
Simple posicast control dates back to the 1950s, and posicast techniques have heretofore been used in satellite control systems. One example is precession of spinning satellites. Rather than firing a single pulse to produce a small angular momentum precession, which would excite a nutation resonance to produce nutation equal to the precession, two pulses are used instead, each delivering half of the total desired momentum precession, spaced half a nutation period apart, resulting in zero nutation at the end of the maneuver. In stepper motor controlled gimbaled payloads, a related system is used in a control feedback loop. A error signal is passed through a filter that passes half the signal immediately, and the other half delayed by half of a resonance period of the structural resonance of concern. This proportional plus delay feedback may be viewed as a finite impulse response (FIR) filter that places the first of it's infinite set of zeros at the location of a resonance whose period is twice the period of the filter delay. These technique is referred to as a "deadbeat" control technique, because, in the ideal case, it nulls the system error in finite time. However, there are many types of deadbeat control, and the term "posicast" is a more specific term for the technique of using proportional plus delay filters for the purpose of deadbeat control of second-order oscillators.
One weakness of simple posicast control is that, since it is in some sense a "notch filter" or "zero-pole cancellation" technique, the effectiveness of its attenuation falls off rapidly as the difference between the expected resonance frequency and the actual frequency grows. An analogous problem arises in designing passive nutation dampers for spacecraft manufactured by the assignee of the present invention. The nutation frequency varies significantly over life, and the nutation damping produced by the passive nutation dampers is highly tuned, acting like a notch filter. An often chosen solution has been to use two nutation dampers having distinct tuned frequencies (e.g., 1/4 and 3/4 of the way between the low and high end of the expected frequency range. The result is that the desired nutation damping is obtained over a broader range than would be obtained using two dampers at the same frequency. This technique was published in a paper entitled "Attitude and Payload Control System for the Least Naval Communications Satellite" by Loren Slafer, Rocky Mountain Guidance and Control Conference, Feb. 3, 1982.
The Cook article cited above suggests that posicast filters may be cascaded to handle several resonance frequencies. In view of this suggestion, it was believed that the problem of having a range of frequencies where the resonance could exist could be attacked by using two filters at different frequencies to give attenuation that spanned that frequency range. It was also believed that this solution might meet a goal of providing a specified amount of attenuation over as wide a frequency range as possible better than collocating the two filter frequencies, as suggested in the Singer patent.
In view of the above, it is an objective of the present invention to provide for a method of using staggered posicast filters in satellite control systems, and the like, that reduces resonances produced in the satellite systems during maneuvers.